1. Either works. Much depends on where it is going to be hung on a wall, and whether there are going to be several side-by-side. The cabinet – if made commercially – could have holes for the shelf pins in all 4 sides so it could be hung in either orientation, but this would be defeated by having drawers.
2. Interior should be white, both the back board and all 4 sides. The exterior should be stained wood with a satin finish – if the user really wants to they can over paint the stain and top coat – the reverse is a LOT of hard work to do.
3. Definitely adjustable shelves. Since you are specifying dimensions in cm's, use the standard 'System 32' of holes every 32mm, which is a bit low for 28mm figures if you are trying to cram them in, but it does give room for 54mm figures, which are the 'traditional' size for toy soldiers.
4. Depends. Drawers should be deeper than they are wide, otherwise they tend to twist sideways and jam, even if you use ball bearing slides (DAMHIK). Wider drawers can be sub-divided internally by a variety of systems, most use grooves cut in the drawer sides and sometimes front and back with thing dividers of ply wood, metal or plastic.
Other considerations: How deep is the cabinet going to be? 10cm, 15cm, 20cm? Is it going to hang on wall or stand on another support such as a table or shelf (You can make it to do both with a bit of care. If it is going to stand on another surface it will need to be 15cm or deeper for stability, maybe with a plinth of molding if its not going to be hung.
She is also going to have to decide on a door system – a major failing of IKEA display cases is that they let dust in around the edge of the glass in most of their products, figures really should have a dust free environment. The front could have a hinged door or the back board could either slide out of grooves in the sides or hinge open at the rear, just so long as it seals out dust, but also consider 'lead rot' caused by lack of ventilation (usually in museum cases where the exhibits are not taken out and the cases are not ventilated)
I'd suggest making a couple of flat mockups from cardboard (wood brown coloured) and white paper for starters, to help figure out the drawer configuration, then take the best of those and make a 3D mockup, again out of cardboard and paper. This what is suggested in several of the better modern woodwork design books and web sites, before you commit to cutting actual wood.